Linear hydrodynamics and viscoelasticity of nematic elastomers

(Received 16 October 2000 and Received in final form 10 December 2000)

Abstract We develop a continuum theory of linear viscoelastic
response in oriented monodomain nematic elastomers. The expression
for the dissipation function is analogous to the Leslie-Ericksen
version of anisotropic nematic viscosity; we propose the relations
between the anisotropic rubber moduli and new viscous
coefficients. A new dimensionless number is introduced, which
describes the relative magnitude of viscous and rubber-elastic
torques. In an elastic medium with an independently mobile
internal degree of freedom, the nematic director with its own
relaxation dynamics, the model shows a dramatic decrease in the
dynamic modulus in certain deformation geometries. The degree to
which the storage modulus does not altogether drop to zero is
shown to be both dependent on frequency and to be proportional to
the semi-softness, the non-ideality of a nematic network. We
consider the most interesting geometry for the implementation of
the theory, calculating the dynamic response to an imposed simple
shear and making predictions for effective moduli and
(exceptionally high) loss factors.